I have refined my criteria over the years. I'm a sahm so my au pairs very rarely have sole charge of the DC, so I need an older brother/sister type of person who can play with the DC and tire them out a bit. The DC can't do homework in the same room and they both need me to sit with them while they do it (DS has ASD, takes nearly an hour to do 20 mins of homework and just won't do unless I'm right beside him, DD has reading trouble and may be dyslexic and needs extra literacy work), so our au pair goes off to play with the one child while I do homework with the other.
DS can be quite oppositional/defiant and DD is extremely shy so I look for candidates who have worked in summer camps or coached a sport so they are used to a wide variety of personality types. The au pair who is starting in June is a Tae Kwon Do coach for instance, so he should be able to take a bit of spirited behaviour. I won't consider anyone who's main experience with children is looking after relatives, and I usually discount the ones with a slightly rose-tinted view of childhood.
I quite like candidates who have a clear reason for wanting to learn English, usually they are a recent graduate and need to have English to further their career. I'm less keen on the ones who are drifting from au pair job to au pair job because they're not sure what they want to do with their lives. Spain recently changed the employment criteria for teachers, I think all teachers now have to have a foreign language to a reasonably high level, so there are quite a few newly-qualified teachers looking for an au pair job.
They have to be over 25 for car insurance reasons, I start my age range from 24 though as sometimes I really like the sound of someone who will be turning 25 soon. They also have to have travelled or lived away from home so I know they can mainly sort themselves out and will just need advice and recommendations from me rather than hand-holding and sorting things out for them.
I also like to read a bit of background about them, something about the sports they do or their interests. I like the ones who seem fairly extrovert as I think they will be happier if they make friends and have a good social life here. So mention of team sports, travelling and going to the beach with friends are all good, only solitary stuff like reading, drawing, watching arty films etc might be less suitable for us (but would suit a family in a rural area perhaps).
I've learned not to get too caught up in their qualifications, we had one au pair who had a masters in educational psychology and she was a lovely person but she wasn't used to just playing with children, so she would observe them or try to direct their play rather than joining in with what they were already doing. So for instance she would ask DS "do you want to come and play X with me?" and he would say "no" so she would go away, whereas our other au pairs would look at what DS was up to and say "that looks fun, can I join in?".
I have found it better to wait for au pairs to apply to me on APW, rather than me making first contact.
I always make a long list, usually 10 or 12 candidates, and then Skype interview the four most likely. I have a list of questions that I email to them before the interview so they know what to expect, and I let the DC ask a few questions, usually about favourite football teams and whether they like dogs. I feel that if they can interact with the DC over Skype then there is a better chance that they will get on in real life. Sometimes the Skype is very revealing, I once interviewed a very strong candidate (newly qualified PE teacher who coached a football team) and he looked horrified at the antics of my DC, whereas the guy that we ended up employing laughed himself silly at the same antics and said my DC were hilarious.